Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 2, pp. 189-204.
@article{AIHPA_1994__61_2_189_0,
     author = {Dimassi, Mouez},
     title = {D\'eveloppements asymptotiques pour des perturbations fortes de l'op\'erateur de {Schr\"odinger} p\'eriodique},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {189--204},
     publisher = {Gauthier-Villars},
     volume = {61},
     number = {2},
     year = {1994},
     mrnumber = {1311064},
     zbl = {0827.35091},
     language = {fr},
     url = {http://archive.numdam.org/item/AIHPA_1994__61_2_189_0/}
}
TY  - JOUR
AU  - Dimassi, Mouez
TI  - Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1994
SP  - 189
EP  - 204
VL  - 61
IS  - 2
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPA_1994__61_2_189_0/
LA  - fr
ID  - AIHPA_1994__61_2_189_0
ER  - 
%0 Journal Article
%A Dimassi, Mouez
%T Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique
%J Annales de l'I.H.P. Physique théorique
%D 1994
%P 189-204
%V 61
%N 2
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPA_1994__61_2_189_0/
%G fr
%F AIHPA_1994__61_2_189_0
Dimassi, Mouez. Développements asymptotiques pour des perturbations fortes de l'opérateur de Schrödinger périodique. Annales de l'I.H.P. Physique théorique, Tome 61 (1994) no. 2, pp. 189-204. http://archive.numdam.org/item/AIHPA_1994__61_2_189_0/

[A-D-H] S. Alama, P. Deift, R. Hempel, Eigenvalue branches of the Schrödinger operators H - λω in a gap of σ (H), Comm. Math. Phys., Vol. 121, 1989, pp. 291-321. | MR | Zbl

[Bi] M. Sh. Birman: [1] Discret spectrum in the gap of the continuous one in the large coupling limit, Oper. Theory: Adv. Appl., Vol. 46, 1990, pp. 17-25.[2] The discret spectrum in a gap of the perturbed periodic operator at large coupling constants, Proc. Conf. Rigorous Results in Quantum Dynamics, Liblice Castle, June 11-15, 1990 (to appear).[3] On discret spectrum in gaps of a perturbed periodic second order operator, Funktional Anal i Prilozken (to appear). | MR

[B-S] M.S. Birman and M.Z. Solomyak: [1] Estimates for the singular numbers of integral operators, Uspekhi Mat. Nank., Vol. 32, 1977, pp. 17-84,English trans. in Russian Math. Surveys, Vol. 32, 1977, pp. 15-89.[2] Asymptotic behaviour of the spectrum of pseudo-differential operators with anisotropically homogeneous symbols, I, Vestnik Leningrad Uni. Math. Mekh. Astronom., 1977, n° 13, pp. 3-21; II, 1989, n° 3, 5, 10; English trans. in Vestnik Leningrad Univ. Math., Vol. 10, 1982; Vol. 12, 1980.[3] Negative discret spectrum of the Schrödinger operator with large coupling constant: a qualitative discussion, Ope. Theory: Adv. App., Vol. 46, 1990, pp. 3-16.[4] Schrôdinger operator. Estimates for the number of the bound states as a function-theoretic problem, Lectures of the XIV School on operator theory and Funciton Spaces, I, Novgorod, 1990; English trans., Amer. Math. Soc., Providence RI (to appear).[5] Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations, Advances in Soviet Mathematics, Vol. 7, 1991. | MR

[D-H] P.A. Deift and R. Hempel, On the existence of eigenvalue of the Schrödinger operator (H - λW) in a spectral gap of, Comm. Math. Phys., Vol. 103, 1986, pp. 461-490. | MR | Zbl

[Di] M. Dimassi, Développements asymptotiques des perturbations lentes de l'opérateur de Schrôdinger périodique, à paraître dans Comm. in P.D.E., 1993. | Zbl

[G-S] F. Gesztesy, B. Simon, On a theorem of Deift and Hempel, Comm. Math. Phys., Vol. 118, 1988, pp. 597-634. | MR

[He-Sj] B. Helffer, J. Sjöstrand, Équation de Schrödinger avec champ magnétique fort et équation de Harper, Preprint Juin 1988.

[H] R. Hempel, On the asymptotic distribution of the eigenvalue branches of a Schrödinger operator (H - λW) in a spectral gap of H, J. Reine Angew. Math., Vol. 399, 1989, pp. 38-59. | MR | Zbl

[K-M] W. Kirsh, F. Martinelli, On the density of states of Schrödinger operators with a random potential, J. Phys. A. Math. Gen., Vol. 15, 1982, pp. 2139-2156. | MR | Zbl

[Re-Si] M. Reed, B. Simon, Methods of modern mathematical physics, I-IV, Academic Press, pp. 1974-1979. | MR

[Sh] M.A. Shubin, The spectral theory and the index of elliptic operators with almost periodic-coefficients, Russian Math. Surveys, Vol. 34, 1979, pp. 109-157. | MR | Zbl

[Sj] J. Sjöstrand, Microlocal analysis for the periodic magnetic Schrôdinger equation and related questions, Lectures Notes in Mathematics, Vol. 1495, 1989, pp. 237- 332. | MR | Zbl

[So] A.V. Sobolev, Weyl asymptotics for the discret spectrum of the perturbed Hill operator, Advances in Soviet Mathematics, Vol. 7, 1991, pp. 159-178. | MR | Zbl